Regularization independent of the noise level: an analysis of quasi-optimality
Regularization independent of the noise level: an analysis of quasi-optimality
复制标题
与噪声水平无关的正则化：准最优性分析
DOI：
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发表时间：
2007
期刊：
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通讯作者：
M. Reiß
中科院分区：
文献类型：
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作者：
F. Bauer;M. Reiß
拟最优性准则选择反问题中的正则化参数，而不考虑噪声水平。这个规则在实践中非常有效，尽管Bakushinskii已经证明了总是有性能非常差的反例。我们提出了一个平均的情况下分析的准最优谱截断估计（也称为截断奇异值分解，TSVD），我们证明了准最优准则确定估计是率最优的平均。它的实际性能说明了一个校准问题，从数学金融。
The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cut-off estimators (also known as truncated singular value decomposition, TSVD) and we prove that the quasi-optimality criterion determines estimators which are rate-optimal on average. Its practical performance is illustrated with a calibration problem from mathematical finance.